Jeff Gau’s research while affiliated with Georgia Institute of Technology and other places

Flying insects are thought to achieve energy-efficient flapping flight by storing and releasing elastic energy in their muscles, tendons, and thorax. However, ‘spring-wing’ flight systems consisting of elastic elements coupled to nonlinear, unsteady aerodynamic forces present possible challenges to generating stable and responsive wing motion. The energetic efficiency from resonance in insect flight is tied to the Weis-Fogh number (N), which is the ratio of peak inertial force to aerodynamic force. In this paper, we present experiments and modeling to study how resonance efficiency (which increases with N) influences the control responsiveness and perturbation resistance of flapping wingbeats. In our first experiments, we provide a step change in the input forcing amplitude to a series-elastic spring-wing system and observe the response time of the wing amplitude increase. In our second experiments we provide an external fluid flow directed at the flapping wing and study the perturbed steady-state wing motion. We evaluate both experiments across Weis-Fogh numbers from 1<N<10. The results indicate that spring-wing systems designed for maximum energetic efficiency also experience trade-offs in agility and stability as the Weis-Fogh number increases. Our results demonstrate that energetic efficiency and wing maneuverability are in conflict in resonant spring-wing systems, suggesting that mechanical resonance presents tradeoffs in insect flight control and stability.

Since taking flight, insects have undergone repeated evolutionary transitions between two seemingly distinct flight modes1–3. Some insects neurally activate their muscles synchronously with each wingstroke. However, many insects have achieved wingbeat frequencies beyond the speed limit of typical neuromuscular systems by evolving flight muscles that are asynchronous with neural activation and activate in response to mechanical stretch2–8. These modes reflect the two fundamental ways of generating rhythmic movement: time-periodic forcing versus emergent oscillations from self-excitation8–10. How repeated evolutionary transitions have occurred and what governs the switching between these distinct modes remain unknown. Here we find that, despite widespread asynchronous actuation in insects across the phylogeny3,6, asynchrony probably evolved only once at the order level, with many reversions to the ancestral, synchronous mode. A synchronous moth species, evolved from an asynchronous ancestor, still preserves the stretch-activated muscle physiology. Numerical and robophysical analyses of a unified biophysical framework reveal that rather than a dichotomy, these two modes are two regimes of the same dynamics. Insects can transition between flight modes across a bridge in physiological parameter space. Finally, we integrate these two actuation modes into an insect-scale robot11–13 that enables transitions between modes and unlocks a new self-excited wingstroke strategy for engineered flight. Together, this framework accounts for repeated transitions in insect flight evolution and shows how flight modes can flip with changes in physiological parameters.

Blinking, the transient occlusion of the eye by one or more membranes, serves several functions including wetting, protecting, and cleaning the eye. This behavior is seen in nearly all living tetrapods and absent in other extant sarcopterygian lineages suggesting that it might have arisen during the water-to-land transition. Unfortunately, our understanding of the origin of blinking has been limited by a lack of known anatomical correlates of the behavior in the fossil record and a paucity of comparative functional studies. To understand how and why blinking originates, we leverage mudskippers (Oxudercinae), a clade of amphibious fishes that have convergently evolved blinking. Using microcomputed tomography and histology, we analyzed two mudskipper species, Periophthalmus barbarus and Periophthalmodon septemradiatus, and compared them to the fully aquatic round goby, Neogobius melanostomus. Study of gross anatomy and epithelial microstructure shows that mudskippers have not evolved novel musculature or glands to blink. Behavioral analyses show the blinks of mudskippers are functionally convergent with those of tetrapods: P. barbarus blinks more often under high-evaporation conditions to wet the eye, a blink reflex protects the eye from physical insult, and a single blink can fully clean the cornea of particulates. Thus, eye retraction in concert with a passive occlusal membrane can achieve functions associated with life on land. Osteological correlates of eye retraction are present in the earliest limbed vertebrates, suggesting blinking capability. In both mudskippers and tetrapods, therefore, the origin of this multifunctional innovation is likely explained by selection for increasingly terrestrial lifestyles.

Flying insects have elastic materials within their exoskeletons that could reduce the energetic cost of flight if their wingbeat frequency is matched to a mechanical resonance frequency. Flapping at resonance may be essential across flying insects because of the power demands of small-scale flapping flight. However, building up large-amplitude resonant wingbeats over many wingstrokes may be detrimental for control if the total mechanical energy in the spring-wing system exceeds the per-cycle work capacity of the flight musculature. While the mechanics of the insect flight apparatus can behave as a resonant system, the question of whether insects flap their wings at their resonant frequency remains unanswered. Using previous measurements of body stiffness in the hawkmoth, Manduca sexta , we develop a mechanical model of spring-wing resonance with aerodynamic damping and characterize the hawkmoth's resonant frequency. We find that the hawkmoth's wingbeat frequency is approximately 80% above resonance and remains so when accounting for uncertainty in model parameters. In this regime, hawkmoths may still benefit from elastic energy exchange while enabling control of aerodynamic forces via frequency modulation. We conclude that, while insects use resonant mechanics, tuning wingbeats to a simple resonance peak is not a necessary feature for all centimetre-scale flapping flyers.

Centimetre-scale fliers must contend with the high power requirements of flapping flight. Insects have elastic elements in their thoraxes which may reduce the inertial costs of their flapping wings. Matching wingbeat frequency to a mechanical resonance can be energetically favourable, but also poses control challenges. Many insects use frequency modulation on long timescales, but wingstroke-to-wingstroke modulation of wingbeat frequencies in a resonant spring-wing system is potentially costly because muscles must work against the elastic flight system. Nonetheless, rapid frequency and amplitude modulation may be a useful control modality. The hawkmoth Manduca sexta has an elastic thorax capable of storing and returning significant energy. However, its nervous system also has the potential to modulate the driving frequency of flapping because its flight muscles are synchronous. We tested whether hovering hawkmoths rapidly alter frequency during perturbations with vortex rings. We observed both frequency modulation (32% around mean) and amplitude modulation (37%) occurring over several wingstrokes. Instantaneous phase analysis of wing kinematics revealed that more than 85% of perturbation responses required active changes in neurogenic driving frequency. Unlike their robotic counterparts that abdicate frequency modulation for energy efficiency, synchronous insects use wingstroke-to-wingstroke frequency modulation despite the power demands required for deviating from resonance.

Flapping-wing insects, birds and robots are thought to offset the high power cost of oscillatory wing motion by using elastic elements for energy storage and return. Insects possess highly resilient elastic regions in their flight anatomy that may enable high dynamic efficiency. However, recent experiments highlight losses due to damping in the insect thorax that could reduce the benefit of those elastic elements. We performed experiments on, and simulations of, a dynamically scaled robophysical flapping model with an elastic element and biologically relevant structural damping to elucidate the roles of body mechanics, aerodynamics and actuation in spring-wing energetics. We measured oscillatory flapping-wing dynamics and energetics subject to a range of actuation parameters, system inertia and spring elasticity. To generalize these results, we derive the non-dimensional spring-wing equation of motion and present variables that describe the resonance properties of flapping systems: N , a measure of the relative influence of inertia and aerodynamics, and K ^ , the reduced stiffness. We show that internal damping scales with N , revealing that dynamic efficiency monotonically decreases with increasing N . Based on these results, we introduce a general framework for understanding the roles of internal damping, aerodynamic and inertial forces, and elastic structures within all spring-wing systems.

Centimeter-scale fliers that combine wings with springy elements must contend with the high power requirements and mechanical constraints of flapping wing flight. Insects utilize elastic energy exchange to reduce the inertial costs of flapping wing flight and potentially match wingbeat frequencies to a mechanical resonance. Flying at resonance may be energetically favorable under steady conditions, but it is difficult to modulate the frequency of a resonant system. Evidence suggests that insects utilize frequency modulation over long time scales to adjust aerodynamic forces, but it remains an open question the extent to which insects can modulate frequency on the wingstroke-to-wingstroke timescale. If wingbeat frequencies deviate from resonance, the musculature must work against the elastic flight system, thereby potentially increasing energetic costs. To assess how insects address the simultaneous needs for power and control, we tested the capacity for wingstroke-to-wingstroke wingbeat frequency modulation by perturbing free hovering Manduca sexta with vortex rings while recording high-speed video at 2000 fps. Because hawkmoth flight muscles are synchronous, there is at least the potential for the nervous system to modulate frequency on each wingstroke. We observed ± 16% wingbeat frequency modulation in just a few wing strokes. Via instantaneous phase analysis of wing kinematics, we found that over 85% of perturbation responses required active changes in motor input frequency. Unlike their robotic counterparts that explicitly abdicate frequency modulation in favor of energy efficiency, we find that wingstroke-to-wingstroke frequency modulation is an underappreciated control strategies that complements other strategies for maneuverability and stability in insect flight.

In many insects, wing movements are generated indirectly via exoskeletal deformations. Measurements of inertial and aerodynamic power suggest that elastic recovery of energy between wingstrokes might reduce power requirements of flight. We tested three questions. (1) Can the thorax itself provide significant energy return? (2) Does a simple damped elastic model describe the bulk mechanical behaviour? (3) Are different regions of the thorax specialized for elastic energy exchange? We measured deformation mechanics of the hawkmoth Manduca sexta thorax by recording the force required to sinusoidally deform the thorax over a wide frequency range. Elastic energy storage in the thorax is sufficient to minimize power requirements. However, we find that a structural (frequency-independent) damping model, not a viscoelastic model, best describes the thorax's mechanical properties. We next performed complementary experiments on a structurally damped homogeneous hemisphere. In contrast to the hemispherical shell, we find that mechanical coupling between different regions of the thorax improves energy exchange performance and that local mechanical properties depend on global strain patterns. Specifically, the scutum region provides energy recovery with low dissipation, while the majority of energy loss occurred in the wing hinge region, highlighting the specificity of thorax regions for flight energetics.

In the vast majority of flying insects, wing movements are generated indirectly via the deformations of the exoskeleton. Indirect measurements of inertial and aerodynamic power requirements suggest that elastic energy exchange in spring-like structures may reduce the high power requirements of flight by recovering energy from one wingstroke to the next. We directly measured deformation mechanics and elastic energy storage in a hawkmoth Manduca sexta thorax by recording the force required to deform the thorax over a frequency range encompassing typical wingbeat frequencies. We found that a structural damping model, not a viscoelastic model, accurately describes the thorax's linear spring-like properties and frequency independent dissipation. The energy recovered from thorax deformations is sufficient to minimize flight power requirements. By removing the passive musculature, we find that the exoskeleton determines thorax mechanics. To assess the factors that determine the exoskeleton's spring-like properties, we isolated functional thorax regions, disrupted strain in an otherwise intact thorax, and compared results to a homogeneous hemisphere. We found that mechanical coupling between spatially separated thorax regions improves energy exchange performance. Furthermore, local mechanical properties depend on global strain patterns. Finally, the addition of scutum deformations via indirect actuation provides additional energy recovery without added dissipation.